Modeling first electron transfer

Porphyrin complexes are particularly suitable cores to construct dendrimers and to investigate how the behavior of an electroactive species is modified when surrounded by dendritic branches. In particular, dendritic porphyrins can be regarded as models for electron-transfer proteins like cytochrome c [42, 43]. Electrochemical investigation on Zn-porphyrins bearing polyether-amide branches has shown that the first reduction and oxidation processes are affected by the electron-rich microenvironment created by the dendritic branches [42]. Furthermore, for the third generation compound all the observed processes become irreversible. 

The reducing character of the ligand is linearly related to the relative position of the first spin-allowed transition and the first electron transfer transition. Jorgensen 233) calculated the optical electronegativity of ethyl-dsep as 2.6 which is close to that of ethyl-dtp, 2.7. Jorgensen 233) has also discussed electron delocalization in M(X2P)3 (X = S, Se) chromophores in terms of a molecular orbital model. 

Why did we introduce this purely experimental material into a chapter that emphasizes theoretical considerations It is because the ability to replicate Tafel s law is the first requirement of any theory in electrode kinetics. It represents a filter that may be used to discard models of electron transfer which predict current-potential relations that are not observed, i.e., do not predict Tafel s law as the behavior of the current overpotential reaction free of control by transport in solution. 

Li and Balbuena conducted a study of the first electron transfer step (Eq. 47) using the DFT method with a catalyst model of five Pt atoms.105... 

Microscopic models of electron transfer processes aim to provide a connection between the nature of the system and the electron transfer event that is lacking in BV. This enables us to rationalize experimental data in terms of the molecular properties of the system as well as to make predictions. Such approaches include first-principles basis for the calculation of the corresponding energy surface and the identification of the fundamental factors behind the activation barrier and the meaning of the reaction coordinate. 

Electron transfer reactions at metal electrodes had been studied long before investigations of processes at semiconductor electrodes were started. They were even studied long before Marcus published his model of electron transfer processes. Early in this century, kinetic models on electron transfer processes had already been developed, which are still used for analyzing experimental data obtained with metal electrodes. Since the corresponding descriptions of the electrochemical kinetics and the application of various techniques are also of importance in semiconductor electrochemistry, the essential results obtained with metal electrodes will be briefly presented in the first section. 

Relative activities for reaction (4.2) over a wide range of semiconductors are given in Table 4.6. Several important points emerge from the data in Table 4.6. First, pdype oxides are more active than n type oxides. This is consistent with the model of electron transfer to the catalyst. Second, the... 

Modeling the First Electron Transfer from Qa to Qb in Reaction Center Proteins from Rb, sphaeroides... 

Wang and Balbuena [86] performed an AIMD study of the first electron transfer step O2+ H (H20)3 /Pt(lll) at 350 K. For the initial configuration, the oxygen was placed parallel to the Pt(l 11) surface at a distance of 3.5A, while the hydrated proton (H (H20)3) was 2.55 A farther away from the O2. With fliis model, they discovered that the proton transfer took place first, then end-on chemisorption was observed, which induced the electron transfer from the slab. Finally, the H-O-0-Ptn dissociated into H-O and O without a clear barrier. 

Our model is based on the associative mechanism, which has substantial experimental and theoretical support, and assumes that the first electron transfer is the rate-determining step. The following simplified reactions are involved ... 

Note that in this model, we only consider the scenario in which the first electron transfer (reaction (6.37)) is the rate-determining step, which is the general case. Under different potentials and operating conditions, it is possible that another step, either chemical or electrochemical, is the ratedetermining step. Therefore, different cases can be developed to study other scenarios. 

The proposed model for the so-called sodium-potassium pump should be regarded as a first tentative attempt to stimulate the well-informed specialists in that field to investigate the details, i.e., the exact form of the sodium and potassium current-voltage curves at the inner and outer membrane surfaces to demonstrate the excitability (e.g. N, S or Z shaped) connected with changes in the conductance and ion fluxes with this model. To date, the latter is explained by the theory of Hodgkin and Huxley U1) which does not take into account the possibility of solid-state conduction and the fact that a fraction of Na+ in nerves is complexed as indicated by NMR-studies 124). As shown by Iljuschenko and Mirkin 106), the stationary-state approach also considers electron transfer reactions at semiconductors like those of ionselective membranes. It is hoped that this article may facilitate the translation of concepts from the domain of electrodes in corrosion research to membrane research. 

These ideas can be applied to electrochemical reactions, treating the electrode as one of the reacting partners. There is, however, an important difference electrodes are electronic conductors and do not posses discrete electronic levels but electronic bands. In particular, metal electrodes, to which we restrict our subsequent treatment, have a wide band of states near the Fermi level. Thus, a model Hamiltonian for electron transfer must contains terms for an electronic level on the reactant, a band of states on the metal, and interaction terms. It can be conveniently written in second quantized form, as was first proposed by one of the authors [Schmickler, 1986] ... 

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